A stabilized semi-implicit fractional step algorithm based on the ﬁnite element method for solving ship wave problems using unstructured meshes is presented. The stabilized governing equations for the viscous incompressible ﬂuid and the free surface are derived at a differential level via a ﬁnite calculus procedure. This allows us to obtain a stabilized numerical solution scheme. Some particular aspects of the problem solution, such as the mesh updating procedure and the transom stern treatment, are presented. Examples of the efﬁciency of the semi-implicit algorithm for the analysis of ship hydrodynamics problems are presented.

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